6 papers
First-Order Analysis of Optimization in Uniformly Convex Metric Spaces: Directional Subderivatives and Basic Descent
D. Russell Luke, Titus Pinta, Qinyu Yan
We develop tools for the analysis and implementation of explicit first-order methods for minimizing functions in uniformly convex metric spaces. We formulate sufficient conditions…
A Newton-Kantorovich Inverse Function Theorem in Quasi-Metric Spaces
Titus Pinta
The purpose of this work is to investigate root finding problems defined on (quasi-)metric spaces, and ranging in Euclidean spaces. The motivation for this line of inquiry stems fr…
A Newton-type Method for Non-smooth Under-determined Systems of Equations
Titus Pinta
We study a variant of Newton's algorithm applied to under-determined systems of non-smooth equations. The notion of regularity employed in our work is based on Newton differentiabi…
A Stochastic Newton-type Method for Non-smooth Optimization
Titus Pinta
We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (appro…
An extension of the second order dynamical system that models Nesterov's convex gradient method
Cristian Daniel Alecsa, Szilárd Csaba László, Titus Pinţa
In this paper we deal with a general second order continuous dynamical system associated to a convex minimization problem with a Frèchet differentiable objective function. We show…
New optimization algorithms for neural network training using operator splitting techniques
Cristian Daniel Alecsa, Titus Pinta, Imre Boros
In the following paper we present a new type of optimization algorithms adapted for neural network training. These algorithms are based upon sequential operator splitting technique…